
	Item 24 Anchor Papers

HSA 2006 Algebra/Data Analysis Item 24

CID: CID92e8ac6f6933771e568b18699f1ddeab
itemNum: 24
initialLetter
itemType: ECR
itemAnswerKey: N/A
itemMaxScorePoints: 4
origNum: x

The table below shows the relationship between the average temperature in March and the date in April when the cherry trees bloom in Washington, D.C.

Complete the following in the Answer Book:
(If you choose to draw a graph to help write the equation, use the grid provided in the Answer Book.)

Write an equation of a line of best fit for the data.
According to your equation, what would be the date in April of the bloom if the average March temperature were 3.5°C? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
Suppose the average March temperature is 14°C. Is it appropriate to use your equation to predict the date in April when the cherry trees will bloom in Washington, D.C.? Use mathematics to justify your answer.

Score Level 1 Anchor Paper
This response indicates little application of a reasonable strategy. Although in the form of an algebraic expression rather than an equation, the representation is essentially correct (–4.5x+32.67). There is no indication that the student has responded to the second or third parts of the question. This response demonstrates a minimal understanding and analysis of the problem.
Score Level 1 Anchor Paper
This response indicates little application of a reasonable strategy. An equation for the line of best fit is not given. While the date in April, if the average March temperature were 3.5°C, is incorrect (April 22), the graphic explanation supports the solution. Although the axes are reversed and the graph lacks labels, the student has correctly plotted the points, drawn a line of best fit and written (I looked at the line of best fit to find my answer). The student states that it is appropriate to use the equation if the March temperature were 14°C, but gives an incomplete justification of the inappropriateness of using the equation (the table doesn't give you the data you need to find the date). This response demonstrates a minimal understanding and analysis of the problem.
Score Level 2 Anchor Paper
This response indicates an incomplete application of a reasonable strategy. The student gives a correct equation for the line of best fit (y=–4.5x+32.7). The date in April, if the average March temperature were 3.5°C, is correct (17^th); however, an explanation is not given. Although the student correctly states that it is inappropriate to use the equation if the average March temperature were 14°C, the justification is incorrect. This response demonstrates a conceptual understanding and analysis of the problem.
Score Level 2 Anchor Paper
This response indicates an incomplete application of a reasonable strategy. An equation for the line of best fit is not given. The date in April, if the average March temperature were 3.5°C, is correct (17^th) and the explanation supports the solution. Although the axes are reversed, the student has labeled the axes, plotted some points, drawn a line of best fit and written (going to the graph and looking for 3.5°C and looked for the intersection on the line of best fit). The student indicates that it is inappropriate to use the equation if the average March temperature were 14°C and the justification supports the solution (the other numbers are so far off of 14°C). This response demonstrates a conceptual understanding and analysis of the problem.
Score Level 3 Anchor Paper
This response indicates application of a reasonable strategy that leads to some correct solutions. Although in the form of an algebraic expression rather than an equation, the representation is essentially correct (–4.45791x+32.66801). The date in April, if the average March temperature were 3.5°C, is correct (17^th of April) and the explanation supports the solution. The student replaces x in the equation with 3.5 and solves for D. The student states that it is inappropriate to use the equation if the average March temperature were 14°C and the justification supports the solution but is incomplete (the data will be different so you would have a different line of best fit). This response demonstrates a clear understanding and analysis of the problem.
Score Level 3 Anchor Paper
This response indicates application of a reasonable strategy that leads to some correct solutions. The student gives a correct equation for the line of best fit (y=–4.458x+32.668). The date in April, if the average March temperature were 3.5°C, is correct (17 day of April) and the explanation is well developed. The student replaces x in the equation with 3.5 and solves for y. The student states that it is inappropriate to use the equation if the average March temperature were 14°C and while the justification supports the solution, it is not mathematical (The trees would bloom in March or February instead of April. So the equation would be useless). This response demonstrates a clear understanding and analysis of the problem.
Score Level 4 Anchor Paper
This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The student gives a correct equation for the line of best fit (y=–4.45x+32.67). The date in April, if the average March temperature were 3.5°C, is correct (April 17) and the explanation is clearly presented. The student replaces x in the equation with 3.5 and solves for y. The student states that it is inappropriate to use the equation if the average March temperature were 14°C and the justification is fully developed (The general pattern for the cherry trees blooming is that the hotter the temperature, the earlier the cherry trees bloom. It shows that when it was 6.2°C in March the cherry trees bloomed on April 3. This led me to believe the trees would bloom in March if the temperature was 14°C). This response demonstrates a complete understanding and analysis of the problem.
Score Level 4 Anchor Paper
This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The student gives a correct equation for the line of best fit (y=–4.46x+32.67). The date in April, if the average March temperature were 3.5°C, is correct (17 of April) and the explanation is well developed. The student replaces x in the equation with 3.5 and solves for y. The student states that it is inappropriate to use the equation if the average March temperature were 14°C and the justification is fully developed (the temp. of 14°C is way off the equation and also off the line of best fit so you would get a wrong answer if used. I got –29.77 which of course is wrong because there is no –29.77 day in April). This response demonstrates a complete understanding and analysis of the problem.

Anchor Papers ~ Algebra/Data Analysis ~ Item 24

HSA 2006 Algebra/Data Analysis Item 24

CID: CID92e8ac6f6933771e568b18699f1ddeab
itemNum: 24
initialLetter
itemType: ECR
itemAnswerKey: N/A
itemMaxScorePoints: 4
origNum: x

The table below shows the relationship between the average temperature in March and the date in April when the cherry trees bloom in Washington, D.C.

Complete the following in the Answer Book:
(If you choose to draw a graph to help write the equation, use the grid provided in the Answer Book.)

Write an equation of a line of best fit for the data.
According to your equation, what would be the date in April of the bloom if the average March temperature were 3.5°C? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
Suppose the average March temperature is 14°C. Is it appropriate to use your equation to predict the date in April when the cherry trees will bloom in Washington, D.C.? Use mathematics to justify your answer.

Score Level 1 Anchor Paper
This response indicates little application of a reasonable strategy. Although in the form of an algebraic expression rather than an equation, the representation is essentially correct (–4.5x+32.67). There is no indication that the student has responded to the second or third parts of the question. This response demonstrates a minimal understanding and analysis of the problem.

Score Level 1 Anchor Paper

This response indicates little application of a reasonable strategy. An equation for the line of best fit is not given. While the date in April, if the average March temperature were 3.5°C, is incorrect (April 22), the graphic explanation supports the solution. Although the axes are reversed and the graph lacks labels, the student has correctly plotted the points, drawn a line of best fit and written (I looked at the line of best fit to find my answer). The student states that it is appropriate to use the equation if the March temperature were 14°C, but gives an incomplete justification of the inappropriateness of using the equation (the table doesn't give you the data you need to find the date). This response demonstrates a minimal understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates an incomplete application of a reasonable strategy. The student gives a correct equation for the line of best fit (y=–4.5x+32.7). The date in April, if the average March temperature were 3.5°C, is correct (17^th); however, an explanation is not given. Although the student correctly states that it is inappropriate to use the equation if the average March temperature were 14°C, the justification is incorrect. This response demonstrates a conceptual understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates an incomplete application of a reasonable strategy. An equation for the line of best fit is not given. The date in April, if the average March temperature were 3.5°C, is correct (17^th) and the explanation supports the solution. Although the axes are reversed, the student has labeled the axes, plotted some points, drawn a line of best fit and written (going to the graph and looking for 3.5°C and looked for the intersection on the line of best fit). The student indicates that it is inappropriate to use the equation if the average March temperature were 14°C and the justification supports the solution (the other numbers are so far off of 14°C). This response demonstrates a conceptual understanding and analysis of the problem.

Score Level 3 Anchor Paper

This response indicates application of a reasonable strategy that leads to some correct solutions. Although in the form of an algebraic expression rather than an equation, the representation is essentially correct (–4.45791x+32.66801). The date in April, if the average March temperature were 3.5°C, is correct (17^th of April) and the explanation supports the solution. The student replaces x in the equation with 3.5 and solves for D. The student states that it is inappropriate to use the equation if the average March temperature were 14°C and the justification supports the solution but is incomplete (the data will be different so you would have a different line of best fit). This response demonstrates a clear understanding and analysis of the problem.

Score Level 3 Anchor Paper

This response indicates application of a reasonable strategy that leads to some correct solutions. The student gives a correct equation for the line of best fit (y=–4.458x+32.668). The date in April, if the average March temperature were 3.5°C, is correct (17 day of April) and the explanation is well developed. The student replaces x in the equation with 3.5 and solves for y. The student states that it is inappropriate to use the equation if the average March temperature were 14°C and while the justification supports the solution, it is not mathematical (The trees would bloom in March or February instead of April. So the equation would be useless). This response demonstrates a clear understanding and analysis of the problem.

Score Level 4 Anchor Paper

This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The student gives a correct equation for the line of best fit (y=–4.45x+32.67). The date in April, if the average March temperature were 3.5°C, is correct (April 17) and the explanation is clearly presented. The student replaces x in the equation with 3.5 and solves for y. The student states that it is inappropriate to use the equation if the average March temperature were 14°C and the justification is fully developed (The general pattern for the cherry trees blooming is that the hotter the temperature, the earlier the cherry trees bloom. It shows that when it was 6.2°C in March the cherry trees bloomed on April 3. This led me to believe the trees would bloom in March if the temperature was 14°C). This response demonstrates a complete understanding and analysis of the problem.

Score Level 4 Anchor Paper

This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The student gives a correct equation for the line of best fit (y=–4.46x+32.67). The date in April, if the average March temperature were 3.5°C, is correct (17 of April) and the explanation is well developed. The student replaces x in the equation with 3.5 and solves for y. The student states that it is inappropriate to use the equation if the average March temperature were 14°C and the justification is fully developed (the temp. of 14°C is way off the equation and also off the line of best fit so you would get a wrong answer if used. I got –29.77 which of course is wrong because there is no –29.77 day in April). This response demonstrates a complete understanding and analysis of the problem.